CN111563345B - Particle merging method for micro-discharge numerical simulation based on K-D tree data structure - Google Patents

Particle merging method for micro-discharge numerical simulation based on K-D tree data structure Download PDF

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CN111563345B
CN111563345B CN202010396021.5A CN202010396021A CN111563345B CN 111563345 B CN111563345 B CN 111563345B CN 202010396021 A CN202010396021 A CN 202010396021A CN 111563345 B CN111563345 B CN 111563345B
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金晓林
赵志成
蔡文劲
谷晓梁
黄桃
杨中海
李斌
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Abstract

The invention belongs to the field of micro-discharge effect numerical simulation, and particularly relates to a particle merging method for micro-discharge numerical simulation based on a K-D tree data structure. According to the method, the particles with similar phase spaces are selected and combined by introducing the K-D tree data structure, so that a large error caused by introducing random numbers when the number of the particles is small is avoided; and selecting the electric quantity, the position and the speed of the combined particles based on a Monte Carlo method, ensuring that the spatial distribution of phases before and after combination is basically consistent, and macroscopically ensuring the conservation of total charge, the conservation of total kinetic energy and the conservation of total momentum. The limitation of the sharp increase of the number of particles in the micro-discharge numerical simulation process on the numerical simulation efficiency is finally overcome, the consistency of the macroscopic characteristics of the particles is ensured while the particle scale is reduced, and the method has important significance for researching the physical mechanism in the micro-discharge forming and evolution process, improving the structural design of a microwave device, improving the micro-discharge threshold value and the like; and the steps are simple and easy to implement.

Description

Particle merging method for micro-discharge numerical simulation based on K-D tree data structure
Technical Field
The invention belongs to the field of micro-discharge effect numerical simulation. In the micro-discharge numerical simulation process of the microwave component, a method for improving the simulation efficiency by reducing the number of particles can be used, and particularly, a particle combination method based on a K-D tree data structure can be used.
Background
In a vacuum or near vacuum environment, electrons impact the surface of metal or medium inside a microwave component under the action of a high-power field, and secondary electrons can be generated when the incident energy and angle meet certain conditions. As the impact progresses, the number of electrons increases in avalanche mode, eventually deteriorating the transmission characteristics and even causing the electrons to break down the component, causing permanent damage, which is called a microdischarge effect. The micro-discharge evolution process can be effectively simulated by combining the particle simulation based on the first principle with a secondary electron emission model, and the method has important values for researching micro-discharge threshold and improving device structure.
However, the calculation amount is increased sharply due to avalanche growth of the number of particles in the micro-discharge simulation process of the microwave part. Under the existing hardware condition, in order to overcome the limitation of the sharp increase of the number of particles on the numerical simulation of the complete physical process of micro discharge, a particle merging method is urgently needed to be introduced, so that the number of particles in the simulation process is reduced, the calculation scale is reduced, and the simulation efficiency is effectively improved. The particle merging method is mainly divided into 2 core steps: the selection of the particles to be merged and the attributes (electrical quantity, position and velocity) of the merged particles are updated.
An early particle merging method for micro-discharge numerical simulation is russian roulette method. The selection of the particles to be merged is carried out through random numbers, the probability p is firstly set (the value range of p is (0, 1), if p =1/2, the total number of the particles after merging is reduced to 1/2 of the original number), then all the particles are traversed, the random number R is generated for each particle, when R < p, the particle is reserved, otherwise, the particle is deleted. The particle attribute updating after the combination is to change the reserved particle electric quantity to 1/p times of the original electric quantity, and the position and the speed are not changed. Although the method can reduce the scale of the simulated particles, the particle distribution before and after combination has large difference.
Later, lapenta improved particle incorporation. The particles to be combined are selected fromThe two steps are carried out: firstly, grouping the particles according to the positions and the speeds of the particles, so that the number of each group of particles is appropriate and the attributes of the positions and the speeds of the particles are close to each other, and the fineness of the specific particle grouping depends on the calculation load; and then sequentially selecting the particle pairs to be combined for each group of particles. The particle attribute updating after the combination is to combine the two particles into one particle, and the electric quantity of the two particles is assumed to be q 1 、q 2 At a position of r 1 、r 2 At a velocity v 1 、v 2 And the electric quantity of the combined particles is q = q 1 +q 2 The position is r = (q) 1 r 1 +q 2 r 2 ) V = (q) speed,/q 1 v 1 +q 2 v 2 ) And/q. The method ensures that the total charge conservation, the total momentum conservation and the center of mass are unchanged before and after combination, but the distribution of the velocity space is damaged, and because the combined particles are at the position of the center of mass of the two particles before combination, the particles gather to the center after multiple combinations, so the distribution of the position space is damaged, and a larger error exists.
Disclosure of Invention
Aiming at the defects of the existing particle merging technology in micro-discharge numerical simulation, the invention provides a particle merging method for micro-discharge numerical simulation based on a K-D tree data structure, which selects particles with similar phase spaces for merging by introducing the K-D tree data structure, and avoids larger errors caused by introducing random numbers when the number of the particles is small; and selecting the electric quantity, position and speed of the combined particles based on a Monte Carlo method, ensuring that the spatial distribution of phases before and after combination is basically consistent, and macroscopically ensuring the conservation of total charge, total kinetic energy and total momentum. The particle combination method has simple steps and easy implementation, and is suitable for the numerical simulation of micro-discharge.
The specific implementation steps are as follows:
step 1, establishing a three-dimensional numerical simulation model of micro-discharge of the microwave component, describing a particle motion process through particle simulation, describing a secondary electron generation process through a secondary electron emission model, and combining the particle motion process and the secondary electron emission model to simulate micro-discharge. A vector (a container for sequentially storing data in computer science) is established for storing the electric quantity, the position and the speed of all macro particles.
And 2, increasing the number of particles continuously along with the micro-discharge numerical simulation. Setting a threshold condition for particle merging, for example, when the number of particles reaches a threshold N (N is a positive integer) or when the simulation time reaches T (T is a positive number), merging the particles, where the thresholds N and T may be fixed values or variable values, and the values of N and T are generally the number of particles and time when the particle size reaches a value that cannot bear the computational burden. The specific steps of particle combination are as follows:
step 2.1, establishing a K-D tree by taking information of six dimensions of positions and speeds of particles stored in a vector as nodes of the K-D tree (a data structure of a K-dimensional Euclidean space organization point in computer science), wherein each node of the K-D tree corresponds to the particles in the vector one by one; the node data is (r) x ,r y ,r z ,λv x ,λv y ,λv z ) Wherein r is x ,r y ,r z Is a position component, v x ,v y ,v z For the velocity component, λ is a weighting factor, which may be a fixed value, or may be a variable, and is used to describe the influence of the velocity on the euclidean distance of the K-D tree: the larger the absolute value of lambda is, the larger the influence of the speed on the Euclidean distance of the K-D tree is; otherwise, the influence is smaller, if the ratio of the maximum value in the standard deviations of the three position components to the maximum value in the standard deviations of the three speed components is S, the value range of lambda is [0.1S,10S [ ]]。
And 2.2, marking each particle in the vector, and initializing each particle to be false by using a Boolean variable aggregate to ensure that each particle is combined at most once.
Step 2.3, setting the current particle as a;
if the clustered variable of a is false, carrying out nearest search on a node corresponding to a in the K-D tree to find out a particle b corresponding to the nearest node; if the Euclidean distance between the nodes corresponding to the nodes in the K-D tree of the a and the b is smaller than a preset distance limit D (D is a positive value, can be a fixed value or can be a variable and is used for avoiding merging particles which are too far away, D is not larger than the value of the space grid step length) and the merged variable of the b is false, merging the particles of the a and the b, and setting the merged variable of the a and the b as true; otherwise, the merged variable of a is directly set to true without particle merging.
The method for determining the electric quantity, the position and the speed of the particles after the combination of the a and the b comprises the following steps: let the electric quantities of a and b be q a 、q b At positions respectively r a 、r b At a velocity v respectively a 、v b Then the electric quantity of the combined particles is q a +q b Generating a random number R with a value range of [0, 1); if it is
Figure BDA0002487564590000031
The position and velocity of the particle after combination takes the value r a And v a Otherwise, the position and speed values r b And v b 。
If the merged variable of a is true, then the particle is skipped.
And 2.4, circularly executing the step 2.3 until all the particles are traversed, namely the merge variables of all the particles are true, and finishing the particle merging.
Compared with the existing particle combination method for micro-discharge numerical simulation, the method has the following advantages:
(1) The invention adopts the data structure of the K-D tree to search the nearest particles, ensures that the attributes of the two particles used for combination are most similar under the given limit, ensures that the spatial distribution of each phase of the particles before and after combination is consistent as much as possible, has lower time complexity based on the nearest search of the K-D tree, and can also ensure the consistency of the spatial distribution of each phase of the particles before and after combination when the number of the particles is less compared with the Russian Roulette method.
(2) The method utilizes the Monte Carlo method to determine the positions and the speeds of the particles after combination, and compared with the Lapenta method, the method better ensures the consistency of the spatial distribution of the positions and the speeds of the particles before and after combination.
In conclusion, the invention can overcome the limitation of the sharp increase of the number of particles in the micro-discharge numerical simulation process on the numerical simulation efficiency, reduce the particle scale and ensure the consistency of the macroscopic characteristics of the particles, and has important significance for researching the physical mechanism in the micro-discharge forming and evolution process, improving the structural design of the microwave device and improving the micro-discharge threshold value and the like.
Drawings
FIG. 1 is a dimensional block diagram of an impedance transformer according to an embodiment;
FIG. 2 is a graph comparing the probability distributions of the position components of particles along the x-direction at time instant 4ns in example;
FIG. 3 is a graph comparing the probability distributions of the position components of the particles in the y-direction at the time instant 4ns in example;
FIG. 4 is a graph comparing the probability distributions of the position components of the particles along the z-direction at the time instant 4ns in example;
FIG. 5 is a graph comparing the probability distributions of particle velocity magnitudes at time 4ns in example.
Detailed Description
The present invention will be further described in detail by taking an impedance transformer for fixing surface-emitting particles as an example.
Step 1, establishing a three-dimensional numerical simulation model of micro-discharge of the impedance transformer, wherein the dimensional structure of the model is shown as figure 1, wherein figure 1 (a) is a front view of the impedance transformer, and figure 1 (b) is a side view of the impedance transformer, and the unit is mm. The average power loaded on the port face is 10kW, and the mode is TE 10 The signal frequency of the electromagnetic wave signal of (2) is 9.5GHz, and the rise time is 0.1ns. Considering that the micro-discharge numerical simulation itself describes the secondary electron generation process using random numbers, the results are different each time even if the numerical simulation is performed under the same conditions. Therefore, in order to accurately reflect the change of the particle phase space distribution before and after merging, the particle generation process in the micro-discharge numerical simulation process is replaced by the fixed surface emission particles: 169 emission points are uniformly distributed in a square area on the port face, each emission point emits 81 particles in one emission period, the included angle between the emission direction of the particles and the z-axis is distributed between 0 DEG and 30 DEG, and the velocity along the z-axis is 10 DEG 6 m/s, the electric quantity is-3 e-17C, and the transmitting is carried out once every 100 time steps. The grid step size of the particle simulation is 0.25mm, and the time step size is 4.48266024e-4ns. Establishing a vector for storing all macro particlesThe amount of power, location and speed.
Step 2, the number of particles will increase continuously with the progress of numerical simulation. And setting a threshold condition for particle merging, and performing particle merging when the simulation time reaches an integer nanosecond. The method for combining the particles comprises the following steps:
step 2.1, establishing a K-D tree by taking information of six dimensions of particle position and velocity stored in a vector as nodes of the K-D tree, wherein the node data is (r) x ,r y ,r z ,λv x ,λv y ,λv z ) Wherein r is x ,r y ,r z Is a position component, v x ,v y ,v z Is a velocity component, and λ is a weighting factor set to 10 -6 And s. And each node of the K-D tree corresponds to a particle in the vector one by one.
And 2.2, marking each particle in the vector, wherein the particles are represented by Boolean variable aggregate and are initialized to false, and each particle is ensured to be combined at most once.
Step 2.3, assuming that the current particle is a:
if the merged variable of a is false, performing nearest neighbor search on the node corresponding to a in the K-D tree, finding out the particle b corresponding to the nearest node, if the Euclidean distance between the nodes corresponding to a and b in the K-D tree is smaller than the preset distance limit of 0.25mm and the merged variable of b is false, performing particle merging on a and b, and setting the merged variable of a and b as true, otherwise, not performing particle merging, and directly setting the merged variable of a as true.
The method for determining the electric quantity, the position and the speed of the particles after the combination of the a and the b comprises the following steps: let the electrical quantities of a and b be q a 、q b At positions respectively r a 、r b At a velocity v respectively a 、v b Then the electric quantity of the combined particles is q a +q b Generating a random number R with a value range of [0,1 ], if
Figure BDA0002487564590000041
The position and velocity of the particle after combination takes the value r a And v a Otherwise, the position and speed values r b And v b 。
If the merged variable of a is true, then the particle is skipped.
And 2.4, circularly executing the step 2.3 until all the particles are traversed, namely the merged variables of all the particles are true, so that the particle merging is completed.
Comparing the phase space probability distributions of the particles at different time points under the two conditions of no particle combination and the particle combination method, fig. 2 is a probability distribution comparison graph of the position component of the particles along the x direction at the time point of 4ns in the embodiment, fig. 3 is a probability distribution comparison graph of the position component of the particles along the y direction at the time point of 4ns in the embodiment, fig. 4 is a probability distribution comparison graph of the position component of the particles along the z direction at the time point of 4ns in the embodiment, and fig. 5 is a probability distribution comparison graph of the particle speed magnitude at the time point of 4ns in the embodiment.
Wherein the number of particles without particle combination is 357210, and the number of particles after particle combination method is 1699734. Through comparison, the probability distribution of the particles in the position and velocity phase space is basically kept unchanged after the particle merging method is used, the particle size is reduced to a greater extent, and certain accuracy is guaranteed while the simulation efficiency is improved.

Claims (3)

1. A particle merging method for micro-discharge numerical simulation based on a K-D tree data structure comprises the following specific steps:
step 1, establishing a three-dimensional numerical simulation model of micro-discharge of a microwave component, describing a particle motion process through particle simulation, describing a secondary electron generation process through a secondary electron emission model, and combining the particle motion process and the secondary electron emission model to simulate micro-discharge; establishing a vector for storing the electric quantity, the position and the speed of all macro particles;
step 2, setting a threshold condition of particle merging, and merging particles when the number of the particles reaches a threshold value N or the simulation time reaches T, wherein N is a positive integer and T is a positive number; the specific steps of particle combination are as follows:
step 2.1, establishing a K-D tree by taking information of six dimensions of the position and the speed of the particles stored in the vector as nodes of the K-D tree, wherein each node of the K-D tree corresponds to the particles in the vector one by one;the node data is r x ,r y ,r z ,λv x ,λv y ,λv z Wherein r is x ,r y ,r z Is a position component, v x ,v y ,v z Is the velocity component, λ is the weighting factor; the ratio of the maximum value in the standard deviation of the three position components to the maximum value in the standard deviation of the three speed components is S, and the value of lambda is [0.1S, 10S%]；
Step 2.2, marking each particle in the vector, and initializing each particle to false by using a Boolean variable aggregate;
step 2.3, setting the current particle as a;
if the clustered variable of a is false, carrying out nearest search on a node corresponding to a in the K-D tree to find out a particle b corresponding to the nearest node; if the Euclidean distance of the corresponding nodes of a and b in the K-D tree is smaller than a preset distance limit D and the merged variable of b is false, particle merging is carried out on a and b, the merged variable of a and b is set to true, and D is not larger than the value of the space grid step length; otherwise, directly setting the merged variable of a as true without particle merging;
the method for determining the electric quantity, the position and the speed of the particles after the combination of the a and the b comprises the following steps: let the electric quantities of a and b be q a 、q b At positions respectively r a 、r b Respectively at a velocity v a 、v b Then the electric quantity of the combined particles is q a +q b Generating a random number R with a value range of [0, 1); if it is
Figure FDA0002487564580000011
The position and velocity of the particle after combination take the value r a And v a Otherwise, the position and speed values r b And v b ；
If the merged variable of a is true, skipping the particle;
and 2.4, circularly executing the step 2.3 until all the particles are traversed, namely the merged variables of all the particles are true, so that the particle merging is completed.
2. The particle merge method for microdischarge numerical simulation of claim 1 based on a K-D tree data structure, wherein: in step 2.1, λ = S.
3. The particle merge method for microdischarge numerical simulation of claim 1 based on a K-D tree data structure, wherein: the distance limit d in step 2.3 takes the value of the spatial grid step.
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